Wednesday, January 04, 2006

Pure quantum gravity cannot work

One of the simple - although not quite new - consequences of the "swampland" line of reasoning is that pure theories of quantum gravity cannot work.

This conclusion that we will justify below applies to various loop quantum gravities, spin foams, causal and acausal, dynamical and non-dynamical triangulations, tetrahedronizations, and any other misinterpretations of quantum gravity that you have heard of.

Quantum gravity cannot be studied separately from the other forces, and the other forces cannot be thought of as small corrections to quantum gravity.

On the contrary. In every consistent theory (and background) of quantum gravity,

in the sense that there must exist particles charged under any other kind of force for which the force of gravity is subdominant; their mass/charge ratio is smaller than for extremal black holes and the overall force between two copies of such a particle must be repulsive. This statement may be (and has been) justified by many arguments, for example:

  • the entropy bounds and the absence of remnants
  • the ability of extremal black holes to decay unless they are BPS
  • the continuous character of the magnetic monopole charge of all objects that can be described as black holes
  • the verification that the rule is satisfied in all classes of string theory backgrounds that have been looked at

According to our knowledge of string theory, it seems that there also cannot exist any backgrounds which only contain massless gravity but no massless gauge fields or scalars. See page 6 of the Swampland paper, for example. Pure quantum gravity does not seem to be an option. Moreover, we know that in the real world around us, gravity is not the only force - and the strength of the other forces does not go to zero, not even at the Planck scale.




Let us accept that pure gravity is not the final goal. Can it be a step towards getting a full theory, after we "add" the other forces such as electromagnetism as perturbations?

The answer is a resounding No.

When you add a force that you want to treat perturbatively, which should be possible if the success of QED is reproduced by your quantum theory of gravity and electromagnetism, then you are expanding around "g=0" where "g" is the gauge coupling. In quantum gravity, there is a new ultraviolet cutoff "g.M_{Planck}" above which the effective theory breaks down. If "g" goes to zero, then this scale goes to zero, too. The theory therefore breaks down at all scales. You can't expand around the point where gravity is the strongest force because a quantum theory of gravity in which gravity is stronger than other forces is inconsistent.

In unified theories - i.e. in string theory - this problem is avoided because the same coupling "g" also governs the strength of gravity, and setting "g=0" implies that "M_{Planck}" goes to infinity and the cutoff scale remains finite.

Well, I don't expect that the people who try to study "pure quantum gravity" will suddenly realize and accept these observations. But I do hope that many other readers will get the point. When the role of quantum mechanics is considered, other forces cannot be neglected when we try to include gravity. All forces must be studied simultaneously which is why a unified theory is necessary for a description of quantum gravity to be consistent.

This is the 17th known reason why string theory is the only tool to study quantum gravity, beyond the semiclassical approximation, that we have as of January 2006.

23 comments:

  1. Lubos:

    The notion that gravity is the weakest force you find in the natural world is absolutely wrong. Quite to the contrary, you keep observing the gravity force to be the strongest:

    You see apples fall to the ground all the time. But do you ever see an apple flying to the sky, because it was attracted by electrical force? You observe planets circling the sun due to gravity as the norm. But people never observed a planet being expelled from a star system due to electrical repulsive force, or be attracted to the sun due to attraction of charges. Do you? Occationally you do see a few cases where the EM force is stronger. But overall, there are much more observations of stronger gravity force than anything else.

    Now you may argue that the gravity force between two commonly known fundamental particles are much weaker. But you can NOT define the coupling constant for gravity until you have defined the proper mass scale, so that the gravity coupling constant becomes a dimensionless number, just like alpha is.

    But here is where the theoretical physicists have been strange! In all other occasions, they insist that the natural scale for mass, as for space and time, is the Planck scale. So one Planck mass is the proper mass scale. But then, if you use one Planck mass to define the gravity coupling constant, it is exactly one, so much stronger than the alpha of EM force, which is about 1/137.

    But NO, although they insisted on Planck scale on everything else, when it comes to defining the gravity coupling constant, they changed their mind and refuse to use the Planck mass as the mass scale. Instead, they use something much smaller, something like the proton mass or things like that. Isn't that double standard?

    The correct natural mass scale, as I discovered, is one that when multiplied by the alpha, gives a mass value that equals to the electron mass we know.

    The strength of gravity is defined by the Mach Principle. Consider any particle. The interaction between the particle and the rest of the universe gives an exact total gravitational potential energy which is exactly equal to the mass/energy of the particle. That, is where the equivalence principle comes from, one that says gravity mass and inertia mass is always identical. I have almost everything figure out already. Remember I gave out the formula that G = 1/(2N). Now I can explain completely where that came from, and have also reconciled the remaining 2% discrepancy between theoretical value of G and actual measured value.

    Finally, the hypothesis you raised together with Vafa is uninteresting and unworthy of discussion. A counter example could easily be proposed by a 6 year old little girl. A black hole, for it exhibits no internal property or internal structure at all, can hence be regarded as one single particle (that's what "particle" means). Such a particle can give you any value of M/Q you want.


    Quantoken

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  2. I read the paper yesterday night, but I was unable to meet some useful comment to do so I refrained from just joking at the 01001 number. BTW, I haven't read it when I did the comment about decays.

    As for semiclassical and classical limits, I would like that any comment entering in this discusion made explicit all the constants, no h=c=1 in the limit where c->0 or so.

    About gravity, I thought I was already done with the field, my only contributions being the Quantum Haiku gr-qc/0404086 and the d=24 normalization paper physics/0409022. But here comes a related thinking your paper suggested me in the bed. I supposse that in the limit c->infinite the spin-2 mediator could be replaced by an scalar, could it? But also in the limit h->0 only scalars can remain (it is different in the classical limit n->infinite). So are there two differents ways to recover Newtonian gravity from quantum gravity?

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  3. Dear Quantoken,

    the Earth attracts the apple because it is a combined gravitational action of 6 x 10^{24} kilograms of matter, and all of which has the same sign of the force.

    Because the Earth is electrically neutral, it does not exert any significant electrostatic force because the contributions cancel. But one can still take a piece of magnet and this small magnet exceeds the gravity of the whole planet. You can ask your nurse to help you with this experiment.

    Gravity at the fundamental level is 10^{44} times weaker or so, and ask someone to calculate this ratio for the electrons.

    Best wishes
    Lubos

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  4. Dear Leucipo,

    when we study forces, we still look at at quantum relativistic physics where all adult people use and always can use the c=hbar=1 units, and we leave discussions about nonrelativistic physics and Apples to Quantoken.

    If you really need to recover the c,hbar factors, there are many good high school textbooks of physics.

    All the best
    Lubos

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  5. This is support of conjecture of finiteness of the volume of moduli spaces. But what about NON-SUSY, NON-GEOMETRIC or NON-KAHLER generic flux compactifications??

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  6. This comment has been removed by a blog administrator.

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  7. Dear Planckeon,

    thanks for your interesting question. Your question is slightly ambiguous because it has no verb. What about them? They're doing fine, thank you.

    If you ask whether they have moduli spaces, then the generic nonSUSY ones do not have one; nonGEOMETRIC backgrounds tend to have less moduli (but they still have moduli if they're e.g. points on the regular moduli spaces, such as Gepner models); and the moduli of nonKähler compactifications are claimed to exist by some colleagues, but disputed by others.

    If you ask whether the bound on the strength of gravity should hold for these three NON classes, the answer is Yes. It should hold generally in quantum gravity. If you asked whether it has been checked on examples, the answer is Partially yes - the heterotic discussion, for example, does not assume Kählerity, geometric interpretation, or spacetime supersymmetry.

    All the best
    Lubos

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  8. Lubos,

    You really do need to see http://feynman137.tripod.com/
    .

    See my blog for Prof Josephson's joke:

    From: "Brian Josephson"
    To: "Nigel Cook"
    Sent: Wednesday, January 04, 2006 4:59 PM
    Subject: Re: mathematics

    ... An old Cambridge story, concerning a person who found himself sitting next to the taciturn Prof. X (X being variously named as Dirac, Stokes ..) at dinner.

    Person sitting next to X: "someone has bet me I won't get more than 2 words out of you tonight"

    Prof. X: "You lose!"

    =b=

    * * * * * * * Prof. Brian D. Josephson :::::::: bdj10@cam.ac.uk
    * Mind-Matter * Cavendish Lab., J J Thomson Ave, Cambridge CB3 0HE, U.K.
    * Unification * voice: +44(0)1223 337260 fax: +44(0)1223 337356
    * Project * WWW: http://www.tcm.phy.cam.ac.uk/~bdj10
    * * * * * * *

    Thanks to Professor Josephson for the joke above! {See footnote to this post for the context of Josephson's email.} The entire physics community is tactiturn and unamused at any innovation. It is nearly as funny as Dr Woit's rip-roaringly scientific response: Thanks to Professor Josephson for the joke above! {See footnote to this post for the context of Josephson's email.} The entire physics community is tactiturn and unamused at any innovation. It is nearly as funny as Dr Woit's rip-roaringly scientific response here:
    http://www.math.columbia.edu/~woit/wordpress/?p=215#comment-4081



    ‘(1). The idea is nonsense. (2). Somebody thought of it before you did. (3). We believed it all the time.’ - Professor R.A. Lyttleton's summary of inexcusable censorship (quoted by Sir Fred Hoyle in ‘Home is Where the Wind Blows’ Oxford University Press, 1997, p154).

    Don't be a tactiturn loser, Lubos!

    Nigel

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  9. Lubos said:
    "Gravity at the fundamental level is 10^{44} times weaker or so, and ask someone to calculate this ratio for the electrons."

    Wrong! It depends on what you call fundamental level. On common dictionary of theoretical physicists, the fundamental level is the Planck Scale. At Planck scale, gravity equals to ONE, roughly 137 times stronger than EM force. On my dictionary, the fundamental scale of mass is roughly 137 times the mass of the electron, and gravity would be 1/2N, i.e., 1/(3x10^40), comparing with 1/137 for EM force. You must be calculating using the electtron mass, but in that case, the gravity is roughly 4x10^42 times weaker than EM force, your 10^44 times figure is still wrong. You would have to use a mass which is roughly 20% of the electron mass to get the 10^44 figure. And certainly if you calculate using proton mass, it's yet a different figure.

    It's chaotic that theoretical physicists can't decide on what to use to calculate the strength of gravity. Some use Planck mass, some use proton mass, some use electron mass. And Lubos is using 20% of electron mass. You guys don't have a clue what is the appropriate mass scale!!! You really can't compare the strength of gravity until you have decided what is the proper mass scale.

    Quantoken

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  10. Quantoken,

    You need to stop talking about the strength of gravity, because it is just embarrassing for everyone. OK?

    Nigel

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  11. Nigel, quantoken does raise the valid point that gravity at first glance should be stronger than EM by that 1 vs 1/137 margin. A fudge factor has to be thrown in to make gravity weaker. The justification for the fudge factor could be something like gravitons get eaten by virtual Planck mass black holes, not that I really understand that, probably cause that nasty vacuum is involved.

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  12. John,

    See http://feynman137.tripod.com/

    (which Quantoken dismisses without reading).

    The reason for the weakness of gravity is down to mechanism. Gauge bosons are always being exchanged between charges and mass, according to quantum field theory. There are two ways they can add up, which gives the tremendous difference in forces.

    Nigel

    http://electrogravity.blogspot.com/

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  13. I don't mind admitting I am a newbie, but I wanted to ask if there may be a connection between the (possible) unification of fundamental forces under black hole conditions (on the one side) and the necessity for unifying quantum theory and general relativity to probe the nature of black holes (on the other)? In other words, could quantum gravity only differ from the current theories when unification is a factor? Thanks!

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  14. Dear Newbie,

    in general, yes, black hole physics may reveal features of unification. On the other hand, one must be more explicit about the statements how these features are revealed - some of the detailed implementations of your program can't work.

    For example, at the semiclassical level, a large black hole - at least everywhere outside its event horizon - is fully controlled by the low-energy (long-distance) approximate laws of physics.

    That's because the curvature remains small at all times - relatively to the fundamental mass scales (the curvature radius remains large) - and the low-energy description appropriate for small curvatures remains applicable.

    On the other hand, a tiny black hole near the end of its evaporation process surely tells us about the detailed spectrum near the Planck scale. If we could measure or determine all the correlations of the Hawking radiation in detail, we would learn about the details of quantum gravity, too.

    Meanwhile, the quantum gravity and unification of gravity with other forces is important 1) near the black hole singularity inside the black hole, and 2) for translations between the infalling observer's coordinates and the Schwarzschild coordinates.

    The former is true because the curvature etc. becomes huge near the singularity. The latter is true because there is a divergent redshift factor near the event horizon which translates ordinary frequencies in one frame to huge, Planckian frequencies in the other frame.

    Meanwhile, there is a lot of qualitative observations one can make about the unification of gravity with other forces by looking at black hole physics, see e.g. our weak gravity conjecture.

    So some of the links of the type you mention surely do exist and they're very deep, but life doesn't end with this Yes answer. ;-) There are also many But's, many butts, and so on.

    Best wishes
    Lubos

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  15. Thanks for the quick and thoughtful response to my question. I am currently studying your paper at http://arxiv.org/abs/hep-th/0601001 - I think it may take me a while to understand it sufficiently to make a further comment on this.

    (One thought experiment that occurred to me was as follows: one of two entangled particles has passed the event horizon when the wave function of the other particle is collapsed. Is there any frame of reference in which the two particles can be seen to comply with the currently understood laws of QM? If not, could this point to QM breaking down in some way inside the event horizon?) Thanks again!

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  16. Dear Newbie01,

    quantum mechanics never break down.

    Experiments with entangled particles involving black holes are surely exciting. But you should try to understand that the black hole horizon guarantees that there will be fewer possible paradoxes, not more paradoxes!

    Of course that the measured entangled particles will remain correlated, just like QM predicts. General relativity guarantees that physics near the horizon of a large black hole, in a freely falling frame, must be indistinguishable from physics outside gravitational fields. That's the equivalence principle - a remarkably accurately tested pillar of modern physics.

    Because physics outside gravitational fields implies all the correlations between the entangled particles - for various decisions what you measure - these things must hold even if one of those particles is inside a black hole, otherwise the equivalence principle would be broken.

    These are very robust things. Can you explain a rational reason why you think that something should go wrong with QM involving entangled pairs and event horizons? So far you have surely not found any hint for a room for any contradiction or violation of QM.

    The very point of quantum gravity is that both the postulates of quantum mechanics as well as basic rules of general relativity such as the equivalence principle remain intact. And one can demonstrate that this is actually a consistent combination. The only thing that is slightly modified is that the causal rules of an evaporating black hole are violated by tiny correlations that guarantee that the information gets out.

    But there can't be any low-energy measurable effects - differences from normal EPR experiments - that would allow you to determine that you have crossed the event horizon - otherwise the equivalence principle and locality and many other things would be brutally broken which is almost certainly impossible.

    Best wishes
    Lubos

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  17. I forgot to explain why event horizons make the number of possible measurable paradoxes smaller, not larger.

    It's because the observers who stay outside the black hole can never directly observe what happened inside the black hole - causality. Because they can see less, they can also see fewer contradictions.

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  18. Hi again - thanks for your answer, which is very clear. I am not clear about the current "mainstream" views on quantum mechanics, but I what I meant to say was that if one held that quantum mechanics explains only observable phenomena and nothing else, then one gets into trouble with the internal dynamics of black holes. If one says that the pair of entangled particles are still entangled, in spite of the impossibility of observing them both, then one is accepting that the process of observation is not fundamental to the process, and that there is an underlying reality, of which our observations are only a part. From your answer above, you see no problem here because you take this as a given. Thanks again for clarifying this.

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  19. Dear newbie, I am not 100% certain whether I understand you but let me try to add a few words:

    There have indeed been big mysteries about the functioning of quantum mechanics in the presence of the black holes, especially the information loss problem. Causality seemed to imply that the information can never get out of the black hole again, leaving the evolution of the world non-unitary after the black hole creates and evaporates.

    This problem has been fixed because the causality is not "strictly" respected - tunneling of the information is possible and is enough to hide the information about the infalling observer in the tiny correlations of the particles of the Hawking radiation.

    Be sure that this is both correct and mainstream viewpoint on the information loss issues as of 2009: the information is not lost. In a similar way, it is believed that there is no inconsistency in any of these quantum effects involving black holes.

    I don't quite follow what your new paradox is/was supposed to be. I agree, and have always agreed, that there is no "reality of a particle" before it's observed. It's only described by a wave function which is not a real wave.

    But of course, when a property of a particle anywhere is measured, the result of this measurement becomes a fact. This fact is obvious to the observers very close to the observations, but it is a matter of other limitations - (approximate) causality etc. - whether this fact can be communicated to others.

    If the measurement was inside a black hole, the fact can't really be told to people outside the black hole. But it's still a fact for the infalling observers, assuming that they can really perceive what they measure. ;-)

    But paradoxes arise if one can compare measurements in different ways, obtaining different predictions for the comparisons. But if the facts about the measured spins etc. can't be communicated, it's harder, not easier, to find an observable paradox.

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  20. Dear Lubos,
    Now I am a bit less clear! I think there are a number of issues that I was trying to clarify by means of the example of entangled particles:
    1. Do the particles exist before they are observed?
    2. Are the particles entangled before they are observed?
    3. Does the impossibility of any human observer observing one of the entangled particles have any effect upon its properties (or the properties of the pair)?
    I would say "Yes, Yes, No" to these three questions. I agree with Einstein's view that quantum mechanics must be incomplete because it only explains a part of the overall reality i.e. our observations of that reality. Einstein kept coming up with thought experiments that he hoped would show up this problem, but each time, Bohr et al overcame Einstein's objections. I guess I am trying to continue that debate, even though I do not claim to have a deep understanding of the subject. (I did a degree in
    Mathematical Physics, but have had no opportunity to build on what I learnt.) Thanks for your time, Tony.

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  21. Dear Tony,

    1) Well, particles exist, except that the detailed information about their state, number, and other properties in a particular situation only exists at the statistical level - as encoded in the wave function - before the measurement. But they surely do exist in the sense that they're useful concepts to understand the real world and real consequences of their existence.

    I don't want to get into vacuous philosophical debates about the meaning of the word "existence" but let me say that I choose to use this verb in such a way that particles surely do exist.

    2) In an experiment with entangled particles that you began with, the particles are entangled, indeed, by the very assumption, unless you redefine the word "entangled" along the way.

    The particles are entangled before the measurement - which means that the subsequent measurements are predicted to be statistically correlated, and will be statistically correlated.

    So I think that the question 1) is tautological. I can't possibly understand what nontrivial question you were trying to ask here, except for the question whether entanglement exists. Yes, it does exist. It is a basic feature of quantum mechanics and our world completely and universally obeys the postulates of quantum mechanics.

    3) Human observers play no privileged role in quantum mechanics that would distinguish them from other macroscopic objects interacting with the particles. Quantum mechanics doesn't use and doesn't need any anthropocentric spiritual flapdoodle.

    The properties of particles, their coherence, interference, entanglement, etc. are affected by the way how they interact with other parts of the system, e.g. with macroscopic objects, but it doesn't matter whether these objects are "human" or not. The predictions are, of course, affected by the (non)existence of the interactions with macroscopic objects.

    At any rate, I think that all these three questions are somewhat physically vacuous and/or their answers are either ill-defined or tautological. Moreover, I don't think that any of these questions has anything to do with gravity or black holes - which were the actual topic of the article under which you posted these comments. ;-)

    Sorry for this criticism.

    Best wishes
    LM

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  22. Hi Lubos - OK, it does seem that my questions arose from a misunderstanding of where QM stands today, so your criticisms are justified. My only excuse is that I had wrongly got the impression (stemming from the way we were taught at University) that QM was based on an anthropocentric approach that could not be applied to black holes. Sorry if I have wasted your time! Tony.

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